Problem: Simplify the following expression: $ q = \dfrac{t + 10}{-8t} - \dfrac{-9}{4} $
Explanation: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{4}{4}$ $ \dfrac{t + 10}{-8t} \times \dfrac{4}{4} = \dfrac{4t + 40}{-32t} $ Multiply the second expression by $\dfrac{-8t}{-8t}$ $ \dfrac{-9}{4} \times \dfrac{-8t}{-8t} = \dfrac{72t}{-32t} $ Therefore $ q = \dfrac{4t + 40}{-32t} - \dfrac{72t}{-32t} $ Now the expressions have the same denominator we can simply subtract the numerators: $q = \dfrac{4t + 40 - 72t }{-32t} $ Distribute the negative sign: $q = \dfrac{4t + 40 - 72t}{-32t}$ $q = \dfrac{-68t + 40}{-32t}$ Simplify the expression by dividing the numerator and denominator by -4: $q = \dfrac{17t - 10}{8t}$